Bounds for rotating convection at infinite Prandtl number from semidefinite programs
A. Tilgner · Physical Review Fluids · 2022
The technique of semidefinite programming is used to replace direct numerical simulations and time integrations of turbulent flows with an optimization problem which is easier to solve but which returns only upper bounds to the time averages the direct numerical simulation would have produced. This idea is applied to rotating Rayleigh-B\'enard convection at infinite Prandtl number. The obtained bounds are not sharp but they reproduce the qualitative behavior of the results known from direct simulations and experiments.